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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.ode.nonstiff;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.20"></a>
<FONT color="green">021</FONT>    <a name="line.21"></a>
<FONT color="green">022</FONT>    <a name="line.22"></a>
<FONT color="green">023</FONT>    /**<a name="line.23"></a>
<FONT color="green">024</FONT>     * This class implements the Gill fourth order Runge-Kutta<a name="line.24"></a>
<FONT color="green">025</FONT>     * integrator for Ordinary Differential Equations .<a name="line.25"></a>
<FONT color="green">026</FONT>    <a name="line.26"></a>
<FONT color="green">027</FONT>     * &lt;p&gt;This method is an explicit Runge-Kutta method, its Butcher-array<a name="line.27"></a>
<FONT color="green">028</FONT>     * is the following one :<a name="line.28"></a>
<FONT color="green">029</FONT>     * &lt;pre&gt;<a name="line.29"></a>
<FONT color="green">030</FONT>     *    0  |    0        0       0      0<a name="line.30"></a>
<FONT color="green">031</FONT>     *   1/2 |   1/2       0       0      0<a name="line.31"></a>
<FONT color="green">032</FONT>     *   1/2 | (q-1)/2  (2-q)/2    0      0<a name="line.32"></a>
<FONT color="green">033</FONT>     *    1  |    0       -q/2  (2+q)/2   0<a name="line.33"></a>
<FONT color="green">034</FONT>     *       |-------------------------------<a name="line.34"></a>
<FONT color="green">035</FONT>     *       |   1/6    (2-q)/6 (2+q)/6  1/6<a name="line.35"></a>
<FONT color="green">036</FONT>     * &lt;/pre&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>     * where q = sqrt(2)&lt;/p&gt;<a name="line.37"></a>
<FONT color="green">038</FONT>     *<a name="line.38"></a>
<FONT color="green">039</FONT>     * @see EulerIntegrator<a name="line.39"></a>
<FONT color="green">040</FONT>     * @see ClassicalRungeKuttaIntegrator<a name="line.40"></a>
<FONT color="green">041</FONT>     * @see MidpointIntegrator<a name="line.41"></a>
<FONT color="green">042</FONT>     * @see ThreeEighthesIntegrator<a name="line.42"></a>
<FONT color="green">043</FONT>     * @version $Id: GillIntegrator.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.43"></a>
<FONT color="green">044</FONT>     * @since 1.2<a name="line.44"></a>
<FONT color="green">045</FONT>     */<a name="line.45"></a>
<FONT color="green">046</FONT>    <a name="line.46"></a>
<FONT color="green">047</FONT>    public class GillIntegrator extends RungeKuttaIntegrator {<a name="line.47"></a>
<FONT color="green">048</FONT>    <a name="line.48"></a>
<FONT color="green">049</FONT>      /** Time steps Butcher array. */<a name="line.49"></a>
<FONT color="green">050</FONT>      private static final double[] STATIC_C = {<a name="line.50"></a>
<FONT color="green">051</FONT>        1.0 / 2.0, 1.0 / 2.0, 1.0<a name="line.51"></a>
<FONT color="green">052</FONT>      };<a name="line.52"></a>
<FONT color="green">053</FONT>    <a name="line.53"></a>
<FONT color="green">054</FONT>      /** Internal weights Butcher array. */<a name="line.54"></a>
<FONT color="green">055</FONT>      private static final double[][] STATIC_A = {<a name="line.55"></a>
<FONT color="green">056</FONT>        { 1.0 / 2.0 },<a name="line.56"></a>
<FONT color="green">057</FONT>        { (FastMath.sqrt(2.0) - 1.0) / 2.0, (2.0 - FastMath.sqrt(2.0)) / 2.0 },<a name="line.57"></a>
<FONT color="green">058</FONT>        { 0.0, -FastMath.sqrt(2.0) / 2.0, (2.0 + FastMath.sqrt(2.0)) / 2.0 }<a name="line.58"></a>
<FONT color="green">059</FONT>      };<a name="line.59"></a>
<FONT color="green">060</FONT>    <a name="line.60"></a>
<FONT color="green">061</FONT>      /** Propagation weights Butcher array. */<a name="line.61"></a>
<FONT color="green">062</FONT>      private static final double[] STATIC_B = {<a name="line.62"></a>
<FONT color="green">063</FONT>        1.0 / 6.0, (2.0 - FastMath.sqrt(2.0)) / 6.0, (2.0 + FastMath.sqrt(2.0)) / 6.0, 1.0 / 6.0<a name="line.63"></a>
<FONT color="green">064</FONT>      };<a name="line.64"></a>
<FONT color="green">065</FONT>    <a name="line.65"></a>
<FONT color="green">066</FONT>      /** Simple constructor.<a name="line.66"></a>
<FONT color="green">067</FONT>       * Build a fourth-order Gill integrator with the given step.<a name="line.67"></a>
<FONT color="green">068</FONT>       * @param step integration step<a name="line.68"></a>
<FONT color="green">069</FONT>       */<a name="line.69"></a>
<FONT color="green">070</FONT>      public GillIntegrator(final double step) {<a name="line.70"></a>
<FONT color="green">071</FONT>        super("Gill", STATIC_C, STATIC_A, STATIC_B, new GillStepInterpolator(), step);<a name="line.71"></a>
<FONT color="green">072</FONT>      }<a name="line.72"></a>
<FONT color="green">073</FONT>    <a name="line.73"></a>
<FONT color="green">074</FONT>    }<a name="line.74"></a>




























































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